**4. Discussion**

The above results showed that the etching of end mills with a fast atom beam allows an appreciable sharpening of the tools. Due to the etching, the cutting edge radius diminishes to ≈3−4 μm from the minimum value of ≈10−11 μm available with the tool sharpening through grinding. The sharpening occurs due to a quite homogeneous sputtering of the tool surface near the edge at low gas pressure *p* < 1 Pa. Homogeneous plasma inside the chamber is generated by the glow discharge with a large hollow cathode [48], which is the vacuum chamber itself.

It was discovered in [49] that the lower limit of the glow discharge operating pressure is proportional to the aperture of electron losses from the hollow cathode, and due to a decrease in the aperture, it can be diminished to ≈0.01 Pa. This finding made it possible to use the discharge for the plasma immersion processing of products [50,51], in broad beam sources of gaseous ions [52–55] and electron beam sources [56–58]. The present research is the first attempt to use the discharge for the micro tools processing.

In our case, the aperture of electron losses is equal to the surface area of the anode immersed in the discharge plasma. The volume of the vacuum chamber with a diameter of 50 cm and length of 55 cm amounts to *V* = 0.12 m3, and its internal surface area is equal to *S* = 1.5 m2. When the anode area *S*<sup>a</sup> is less than a critical value

$$\text{S}^\* = \text{(}\pi/\text{e}\text{)}^{1/2} \text{(}2m/M\text{)}^{1/2} \text{S} \approx \text{(}2m/M\text{)}^{1/2} \text{S} \tag{6}$$

where *S* is the chamber surface area, *m* and *M* are the electron mass and the ion mass, and e is the Naperian base, a positive anode fall of potential *U*<sup>a</sup> occurs [42]. With a pressure decrease from 0.1 to 0.01 Pa, the anode fall can grow from *U*<sup>a</sup> ≈ 10 to *U*<sup>a</sup> ≈ 500 V. It results in the anode overheating and melting by electrons accelerated in the negative space charge sheath near the anode surface.

For the discharge in argon and *S* = 1.5 m2, the critical value amounts to *S*\* = 0.008 m2. Not to have problems with the discharge anode, its surface area was chosen to be equal to *S*<sup>a</sup> = 0.02 m2. This area exceeds the critical anode area of *S*\* = 0.008 m2 and, hence, it prevents the positive anode fall of potential. The discharge plasma uniformity at the gas pressure of 0.01–1 Pa makes it possible to accelerate ions from the main plasma volume in the center of the chamber using a concave grid (Figure 6) and transform the concentrated ion beam into a fast atom beam. The decrease in the cutting edge radius of the end mills after etching with such a beam can be explained in Figure 14.

**Figure 14.** Scheme of etching cutting tools in plasma by accelerated particles.

When a negative voltage is applied to the cutting edge in the plasma, ions are extracted from the plasma and enter the sheath. The width of the sheath at a voltage from 100 to 1000 V exceeds 1 mm. Therefore, the radius of the plasma boundary emitting ions onto the cutting edge surface exceeds about one hundred times the cutting edge radius of 10 μm. In a homogeneous plasma, the ion current density is constant at the entire plasma boundary. However, the area of the plasma emitting ions on the cutting edge is one hundred times larger than the edge area.

Therefore, the ion current density at the edge is a hundred times higher than at the rest of the wedge surface. Etching of the edge leads to a significant increase in its radius, and the tool becomes blunt. To avoid bluntness of the tool, it is necessary to etch not by ions accelerated from the plasma by a voltage applied to the tool but by a broad beam of accelerated ions or fast atoms. They sputter the cutting edge of the tool with the same intensity as the rest of its surface. When removing a surface layer of the same thickness, the radius of the cutting edge decreases. Therefore, the tool is sharpened, when it is etched by a broad beam.

In our experiments, the cutting edge radius diminished to ≈3−4 μm from the minimum value of ≈10−11 μm available at the tool sharpening through grinding. In the beginning, the etching rate amounted to ≈2 μm/h, and after a 3-h-long etching, it diminished to zero. The reason for this phenomenon can be related to the structure of the end mill material. In our case, it was a carbide type HM CK10-20-MG Micrograin of carbide group: tungsten-cobalt single-corpus with the carbide grain size of 0.8 μm. One can hardly imagine a tool with a cutting edge radius of ≈1 μm made of a material with a grain size of 0.8 μm. In our experiments, the minimum cutting edge radius exceeds the grain size by five times.

The results of the end mills etching presented in Table 2 exhibit another specific feature to be explained. They reveal a difference in the dependencies on the etching time of the cutting edge radius for the end mill sections distant from the mill end at 2, 7, and 12 mm. The 12-mm-long cutting part of the end mill rotated in the center of the 20-mm-diameter beam and should be etched quite homogeneously. Nevertheless, the etching rate for the section distant from the mill end at 7 mm was a little higher than for the sections distant from the mill end at 2 and 12 mm. It could be caused by a radial distribution of the fast atom flow density with a maximum at the beam axis.

The use of wear-resistant coatings prevents the intensive wear of the cutting tool; however, the coating affects the microgeometry of the cutting edge by increasing the radius of its rounding. With an increase in the radius of the cutting edge about the thickness of the cut layer, the deformation area of the workpiece increases, and as a result, the force load on the tool tooth increases [31]. Cutting forces have a great influence on the chip formation nature, the process of material cutting, vibration characteristics of cutting, the integrity of the cutting tool, and the surface quality [59–62]. Additional surface treatment by fast atoms will reduce the cutting edge radius and prepare surfaces for the deposition of a wear-resistant coating while providing a relatively smaller radius of the cutting edge than when coating the surface without preparation of this kind.

Unlike the constant undeformed chip thickness (UCT) and direction of cutting speed in orthogonal micro-cutting, both vary in a time-dependent manner in micro-milling. The micro-milling process can be considered as the composition of varied orthogonal micro-cutting in the time domain [63–65]. In end micro-milling (Figure 15a), the thickness (i) initially increases from zero, (ii) reaches the maximum value (approximately equal to the feed per tooth), and (iii) reduces to zero, while in a side micro-milling (Figure 15b), the thickness decreases from maximum to zero. The above stages may occur sequentially for a single cutting edge, or, in most common scenarios, simultaneously for multiple cutting edges depending on the employed tool geometries (the cutting edge radius and tooth number) and the machining parameter (feed per tooth) [66]. This would result in very complex material behaviors in comparison with orthogonal micro-cutting.

**Figure 15.** Tool pass in full immersion (**a**) and side micro-milling process (**b**).

Consider the side micro-milling process based on the two-tooth micro milling cutter as an example. If the UCT at the entrance is larger than the minimum undeformed chip thickness (MUCT), the chip begins to form (Figure 15b). However, when the instantaneous UCT becomes smaller than the MUCT, the chip generation would stop. A part of the workpiece material will elastically recover, while other material will undergo plastic deformation after the micro-milling cutter is passed by. The machined surface in a side micro-milling includes both the theoretical residual height (*R*t) and the residual height (*R*max) left by the existing MUCT (Figure 16b) [62]. *R*max in micro-milling can be expressed as Equation (7) [62], respectively, and they are primarily related to the feed per tooth (*f* z) and MUCT (*h*m), as shown in Equation (8).

**Figure 16.** (**a**) Residual height of residual microroughness (*R*max); (**b**) minimum undeformed chip thickness *h*m; (**c**) forces in the ploughing-dominated region: point I—micro end mill coated after etching by fast atoms, point II—micro end mill coated after grinding.

As a result of using the etching operation before coating, the radius of the cutting edge can be reduced to 6.25 microns compared to 12.7 after coating a ground micro mill.

Reducing the cutting edge radius allows decreasing the height of residual microroughness formed during cutting in the area of the plunger zone from 1.33 μm (point I in Figure 16a) to 0.58 μm (point II in Figure 16a), minimum undeformed chip thickness *h*<sup>m</sup> from 2.97 μm (point I in Figure 16b) to 1.46 μm (point II in Figure 16b), forces in the ploughing-dominated region determined on the base of ref. [65,66] from 7 N/mm (point I in Figure 16c) to 5.7 N/mm (point II in Figure 16c) when machining a steel part with the following parameters β 40◦, Poisson's ratio *k* 0.25 (for steel), mill's radius *R*<sup>f</sup> 1.5 mm, feed

per tooth 0.005 mm/tooth. After the chip thickness of 3.0 μm, where the effect of ploughing becomes small and that of shearing is more significant, forces for pearlite became higher, but increasing these parameters are actual only for the machining process with small deps of cut [67–69].

$$R\_{\text{max}} = \frac{f\_{\text{z}}^2}{8R\_{\text{f}}} + \frac{(1-k)h\_{\text{m}}}{2} \left( 1 + \frac{\left[ (1-k)h\_{\text{m}} \right]^2}{f\_{\text{z}}^2} \right) \tag{7}$$

$$h\_{\rm m} = r(1 - \cos(\beta))\tag{8}$$
